Diffraction grating with reduced polarization-dependent loss

ABSTRACT

A diffraction grating that achieves high diffraction efficiency at all polarizations for optical signals at telecommunications wavelengths is provided. The diffraction grating has a substrate and a plurality of reflective faces oriented at respective blaze angles θ b  spaced along the substrate surface, with the blaze angles substantially differ from the Littrow condition. Each reflective surface is supported by a support wall connected substantially with the substrate surface. The grating may be used in interference orders greater than first order and may diffract signals with low polarization-dependent losses in addition to high polarization-averaged efficiency.

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application is a continuation-in-part application of U.S.patent application Ser. No. 09/615,300 entitled “DIFFRACTION GRATINGWITH REDUCED POLARIZATION-DEPENDENT LOSS,” filed Jul. 13, 2000, by LarryFabiny and Tony Sarto, and a continuation-in-part application of U.S.patent application Ser. No. 09/669,758 entitled “GRATING FABRICATIONPROCESS USING COMBINED CRYSTALLINE-DEPENDENT AND CRYSTALLINE-INDEPENDENTETCHING,” filed Sep. 26, 2000, the disclosures of each of which areincorporated herein by reference in their entirety for all purposes.

BACKGROUND OF THE INVENTION

[0002] This application relates generally to a method and apparatus fordiffracting light, and more specifically to a diffraction grating usefulin various applications, such as optical telecommunications, thatrequire high diffraction efficiency in multiple polarizationorientations.

[0003] The Internet and data communications are causing an explosion inthe global demand for bandwidth. Fiber optic telecommunications systemsare currently deploying a relatively new technology called densewavelength division multiplexing (DWDM) to expand the capacity of newand existing optical fiber systems to help satisfy this demand. In DWDM,multiple wavelengths of light simultaneously transport informationthrough a single optical fiber. Each wavelength operates as anindividual channel carrying a stream of data. The carrying capacity of afiber is multiplied by the number of DWDM channels used. Today, DWDMsystems using up to 80 channels are available from multiplemanufacturers, with more promised in the future.

[0004] Optical wavelength routing functions often use demultiplexing ofa tight stream into its many individual wavelengths, which are thenoptically directed along different paths. Subsequently, differentwavelength signals may then be multiplexed into a common pathway. Withinsuch routing devices, the optical signals are routed between the commonand individual optical pathways by a combination of dispersion andfocusing mechanisms. The focusing mechanism forms discrete images of thecommon pathway in each wavelength of the different optical signals andthe dispersion mechanism relatively displaces the images along a focalline by amounts that vary with the signal wavelength.

[0005] Both phased arrays and reflective diffraction gratings may beused to perform the dispersing functions. While phased arrays areadequate when the number of channels carrying different wavelengthsignals is small, reflective diffraction gratings are generallypreferable when large numbers of channels are used. However, reflectivediffraction gratings tend to exhibit greater polarization sensitivityand since the polarization of optical signals often fluctuates inoptical communication systems, this sensitivity may result in largevariations in transmission efficiency. Loss of information is possibleunless compensating amplification of the signals is used to maintainadequate signal-to-noise ratios. Although polarization sensitivity maygenerally be mitigated by increasing the grating pitch of the reflectivegrating, limitations on the desired wavelength dispersion for signals atoptical telecommunication wavelengths preclude an increase in gratingpitch sufficient to achieve high diffraction efficiency in allpolarization directions.

[0006] It is thus desirable to provide a diffraction grating that canachieve high diffraction efficiency without significant polarizationsensitivity when used at optical telecommunication wavelengths.

SUMMARY OF THE INVENTION

[0007] Embodiments of the present invention provide such a diffractiongrating, achieving high diffraction efficiency in all polarizationstates when used for diffraction of an optical signal attelecommunications wavelengths. The diffraction grating in suchembodiments includes a plurality of spaced triangular protrusions on asubstrate in which reflective faces are blazed at angles θ_(b) that aresubstantially different from the Littrow condition.

[0008] Thus, in one embodiment of the invention, the diffraction gratingis configured to diffract an optical signal of wavelength λ. It has asubstrate and a plurality of reflective faces oriented at respectiveblaze angles θ_(b) spaced along the substrate surface at a gratingdensity 1/d. The blaze angles θ_(b) substantially differ from theLittrow condition sin θ_(b)=λ/2d . Each of these reflective faces issupported by a support wall that is connected with the substrate surfacesuch that the optical signal is reflected essentially only off thereflective faces and not off the support walls. Since the optical signalis reflected off the reflective faces but not the support walls, thediffraction efficiency of certain polarization states is improved.

[0009] In particular embodiments, the support walls are connectedsubstantially normal with the surface of the substrate and in otherembodiments they are connected at an obtuse angle with the substrate.The blaze angles are preferably within the range 50°≦θ_(b)≦70° and morepreferably within the range 50°≦θ_(b)≦60°. The density at which thereflective faces are spaced along the substrate is preferably between700 and 1100 faces/mm and more preferably between 800 and 1000 faces/mm.

[0010] In a certain embodiment, the reflective faces are equally spacedalong the surface of the substrate at density 1/d between 800 and 1000faces/mm without exposing the surface of the substrate, with each of theblaze angles θ_(b) substantially equal to 54.0°. In another embodiment,the reflective faces are equally spaced along the surface of thesubstrate at density 1/d between 800 and 1000 faces/mm such that aportion of the surface of the substrate is exposed between each suchreflective face, with each of the blaze angles θ_(b) substantially equalto 55.8°. In that embodiment, the support walls preferably have analtitude between 1200 and 1400 nm, more preferably substantially equalto 1310 nm.

[0011] In certain other embodiments, the diffraction grating isconfigured to be used to diffract the optical signal in an interferenceorder higher than first order. In one such embodiment useful in secondorder for wavelengths between 1500 and 1600 nm, the reflective faces arespaced at a grating density of approximately 450 faces/mm, with blazeangles substantially equal to 55.8°. A portion of the substrate may beexposed between subsequent reflective faces, defining trenches betweenthe faces. In one embodiment, each trench has a width between 0.50 and0.70 μm. The height of the support walls defines a groove depth, whichin one embodiment is between 2300 and 2500 μm.

[0012] Embodiments of the invention are also directed to a diffractiongrating for diffracting an optical signal with a polarization-dependentloss less than 0.4 dB when the wavelength of the optical signal isbetween 1500 and 1600 nm. In one such embodiment, the grating isconfigured to diffract an optical signal having a wavelength between1530 and 1565 nm with a polarization-dependent loss less than 0.04 dB.

[0013] According to embodiments of the invention, the diffractiongrating is fabricated by forming two sets of parallel trenches in acrystal surface, one made with a crystalline-independent etchingtechnique and the other made with a crystalline-dependent chemicaletchant. The intersection of the two sets of trenches removes materialfrom the crystal surface to produce an etched crystal surface that canbe coated with a reflective material to form the diffraction grating orcan be used as a master for batch fabrication of diffraction gratings.

[0014] In a particular embodiment, the first set of parallel trenches isinitially formed perpendicularly from a surface of a silicon wafer. Thisset of trenches is then filled with a sacrificial material that alsocoats the surface of the wafer. The sacrificial material is subsequentlypatterned lithographically to expose the underlying wafer, with thecrystalline-dependent chemical etchant being applied at the exposedportions. The deposited sacrificial material acts as an etch stop to thechemical etchant. Appropriate techniques for forming the first set ofparallel trenches include reactive ion etching, deep reactive ionetching, and ion milling. Appropriate crystalline-dependent chemicaletchants that preferentially stop etches along [111] orientationsinclude KOH, hydrazine, and ethylene diamine pyrocatechol.

[0015] In another embodiment, plurality of parallel trenches are formedin a crystal surface with a crystalline-independent technique.Sacrificial material is deposited in each of the plurality of trenches,with some of the sacrificial material also being deposited on thecrystal surface. The excess sacrificial material is removed from thecrystal surface, such as by chemical and mechanical polishing (CMP).Subsequently, the crystal surface is exposed to a crystalline-dependentetchant. The resulting structure may be used for fabrication of thediffraction grating. Alternatively, the remaining sacrificial materialmay be removed from the structure before finalizing the gratingfabrication.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] A further understanding of the nature and advantages of thepresent invention may be realized by reference to the remaining portionsof the specification and the drawings wherein like reference labels areused throughout the several drawings to refer to similar components.

[0017]FIG. 1(a) illustrates a right-apex-angle diffraction grating;

[0018]FIG. 1(b) illustrates the shape of a diffraction grating accordingto a full-sawtooth embodiment of the invention;

[0019]FIG. 1(c) illustrates a the shape of a diffraction gratingaccording to a truncated-sawtooth embodiment of the invention;

[0020]FIG. 2 shows results of numerical simulations of diffractionefficiency profiles for a full-sawtooth embodiment in S and Ppolarization configurations;

[0021]FIG. 3 shows results of numerical simulations of diffractionefficiency profiles for a truncated-sawtooth embodiment in S and Ppolarization configurations;

[0022]FIG. 4(a) shows numerical results for the efficiency in S and Ppolarization configurations for a full-sawtooth grating as a function ofblaze angle;

[0023]FIG. 4(b) shows numerical results for the efficiency in S and Ppolarization configurations for a truncated-sawtooth grating as afunction of blaze angle;

[0024]FIG. 5 shows the variation in optimal blaze angle as a function ofgroove density for a full-sawtooth diffraction grating;

[0025]FIG. 6 shows the variation in efficiency in S and P polarizationconfigurations for a full-sawtooth grating as a function of the angle ofincidence of the optical signal;

[0026]FIG. 7(a) shows results of numerical simulations of diffractionefficiency for a truncated-sawtooth embodiment in an S polarizationconfiguration as a function of triangle groove height;

[0027]FIG. 7(b) shows results of numerical simulations of diffractionefficiency for a truncated-sawtooth embodiment in a P polarizationconfiguration as a function of triangle groove height;

[0028]FIG. 8 shows the variation in efficiency in S and P polarizationconfigurations for a full-sawtooth grating at optimal blaze angle as afunction of groove density;

[0029]FIG. 9 shows the effect on efficiency in S and P polarizationconfigurations of allowing the support walls to connect with thesubstrate non-normally;

[0030]FIG. 10(a) shows results of numerical simulations of diffractionefficiency for a truncated-sawtooth embodiment appropriate for use insecond order in an S polarization configuration as a function of trenchwidth;

[0031]FIG. 10(b) shows results of numerical simulations of diffractionefficiency for a truncated-sawtooth embodiment appropriate for use insecond order in a P polarization configuration as a function of trenchwidth;

[0032]FIG. 11 shows results of numerical simulations of diffractionefficiency in S and P polarizations as a function of trench width for atruncated-sawtooth embodiment with a facet angle of 55.8° appropriatefor use in second order;

[0033]FIG. 12 shows results of numerical simulations for the averagepolarization efficiency as a function of wavelength and groove depth fora truncated-sawtooth embodiment with a facet angle of 55.8° appropriatefor use in second order;

[0034]FIG. 13 shows results of numerical simulations for thepolarization-dependent loss as a function of wavelength and groove depthfor a truncated-sawtooth embodiment with a facet angle of 55.8°appropriate for use in second order;

[0035]FIG. 14 shows results of numerical simulations for both theaverage efficiency and polarization-dependent loss as a function ofwavelength for a truncated-sawtooth embodiment with a facet angle of55.8° appropriate for use in second order;

[0036]FIG. 15 shows the steps performed in one embodiment to fabricatethe diffraction grating: part (a) shows a crystal surface with a normalthat defines an angle ψ with respect to the [110] crystallographicdirection; part (b) shows the formation of a first set of trenches usinga crystalline-independent etching technique; part (c) shows the resultof the depositing sacrificial material on the etched crystal surface;part (d) shows exposure of the underlying crystal surface at specificlocations; part (e) shows the result of applying a crystalline-dependentchemical etchant at the exposed locations; and part (i shows theresulting structure after dissolving the sacrificial material andagitating; and

[0037]FIG. 16 shows the steps performed in another embodiment tofabricate the diffraction grating: part (a) shows a crystal surface witha normal that defines an angle ψ with respect to the [110]crystallographic direction; part (b) shows the formation of a first setof trenches using a crystalline-independent etching technique; part (c)shows the result of depositing sacrificial material on the etchedcrystal surface; part (d) shows the result of chemical and mechanicalpolishing to remove the sacrificial material from the crystal surface;part (e) shows the result of subsequently exposing the crystal to acrystalline-dependent chemical etchant; and part (f) shows the resultingstructure after removal of the remaining sacrificial material.

DESCRIPTION OF THE SPECIFIC EMBODIMENTS

[0038] 1. Introduction

[0039] The following description sets forth embodiments of a diffractiongrating that simultaneously achieves high efficiency in multiplepolarization states for a high groove density at opticaltelecommunications wavelengths. Embodiments of the invention can thus beused with a wavelength router to achieve the goals of optical networkingsystems.

[0040] The general functionality of one such optical wavelength routerthat can be used with embodiments of the invention is described indetail in the copending, commonly assigned U.S. patent application,filed Nov. 16, 1999 and assigned Ser. No. 09/442,061, entitled“Wavelength Router,” which is herein incorporated by reference in itsentirety, including the Appendix, for all purposes. As describedtherein, such an optical wavelength router accepts light having aplurality of spectral bands at an input port and selectively directssubsets of the spectral bands to desired ones of a plurality of outputports. Light entering the wavelength router from the input port forms adiverging beam, which includes the different spectral bands. The beam iscollimated, such as by a lens, and directed to a diffraction gratingthat disperses the light so that collimated beams at differentwavelengths are directed at different angles. The high efficiencyachieved by the diffraction grating in multiple polarization statestranslates directly into improved efficiency in operation of thewavelength router. Other uses for the diffraction grating where highefficiency is desirable in multiple polarization states will besimilarly evident to those of skill in the art.

[0041] 2. Diffraction of Optical Signals

[0042] Demultiplexing of an optical signal that contains a plurality ofsignals at different wavelengths may be accomplished with a diffractiongrating with appropriately sized and shaped diffraction grooves. Anexample of such a demultiplexing diffraction grating is illustrated inFIG. 1(a). When illuminated at an angle α from the normal, the grating100 directs light with wavelength λ toward angle β in accordance withthe formula

mλ=d(sinα±sinβ)

[0043] where m is an integral order of interference and d is the gratingperiod. The manner in which incident light will be distributed among thevarious orders of interference depends on the shape and orientation ofthe groove sides and on the relation of wavelength to groove separation.When d{tilde under (<)}λ, diffraction effects predominate in controllingthe intensity distribution among orders, but when d>λ, opticalreflection from the sides of the grooves is more strongly involved.

[0044] Diffraction gratings 100 are manufactured classically with theuse of a ruling engine by burnishing grooves with a diamond stylus in asubstrate 120 or holographically with the use of interference fringesgenerated at the intersection of two laser beams. For high dispersionwith operational wavelengths in the range 1530-1570 nm, commonly used inoptical telecommunications applications, a line density (=1/d) betweenabout 700 and 1100 faces/mm is desirable. Current efforts may extend theoperational wavelength range for optical telecommunications applicationsby about 30 nm on either end of the 1530-1570 range. It is furtherpossible to “blaze” a grating by ruling its grooves to produce multiplereflective faces 112 that reflect a large fraction of the incoming lightof suitably short wavelengths in one general direction. In general, ablazed grating has been understood to refer to one in which the groovesof the diffraction grating are controlled so that the reflective faces112 form one side of right-apex triangles 110, inclined to the substratesurface with an acute blaze angle θ_(b). Obtuse apex angles up to ˜110°are sometimes present in blazed holographic gratings.

[0045] High efficiency is achieved when blazed grating groove profilesare prepared in the Littrow configuration, in which incident anddiffracted rays are autocollimated so that α=β=θ_(b). In this Littrowconfiguration, the diffraction equation for blaze angle θ_(b) thus takesthe simple form${\sin \quad \theta_{b}} = {\frac{m\quad \lambda}{2d}.}$

[0046] For a Littrow grating with line density 1/d≈900 faces/mm, thepreferred blaze angle at telecommunications wavelengths is θ_(b)≈44.2°(i.e. the blaze wavelength in first order is λ≈2d sin θ_(b)≈1550 nm).With this configuration, however, significant differences are found inthe reflection efficiencies for different polarization states. Inparticular, the diffraction efficiency for an S polarization state (alsodescribed as a TM polarization state), in which the electric field ispolarized orthogonal to the grating grooves, is>90%. Typically, however,there is only 30-50% efficiency for a P polarization state (alsodescribed as a TE polarization state), in which the electric field ispolarized parallel to the grating grooves. This relatively poordiffraction efficiency for the P polarization state is a consequence ofboundary conditions imposed on the electric field as it propagatesparallel to the groove edge in the grating.

[0047] 3. High-Efficiency Polarization-Independent ReflectiveDiffraction Grating

[0048]FIG. 1(b) illustrates a first set of embodiments of the invention(referred to herein as the “full-sawtooth” embodiments), which provide ahigh diffraction efficiency for optical signals at telecommunicationswavelengths in both S and P polarization states. The grating of theseembodiments may be used in first order. In the specific full-sawtoothembodiment illustrated in FIG. 1(b), the diffraction grating 150includes multiple reflective faces 162 formed in a substrate 170, eachinclined at blaze angle θ_(b) to the substrate surface. Each reflectiveface 162 is supported by a support wall 164 that is connectedsubstantially normal with the substrate 170. As a result, thediffraction grating 150 has a sawtooth configuration formed in thesubstrate 170 from multiple right-base triangular protrusions.

[0049] In the illustrated embodiment, each of the reflective faces 162is equally spaced along the surface of the substrate 170, with eachreflective face 162 extending through a full spacing period. Thefull-sawtooth embodiment is characterized by the absence of exposure ofthe substrate 170 at the base of the triangles 210 to incident light—thesupport wall 164 supporting each reflective face 162 is also connectedto the adjacent reflective face. In alternative embodiments of thefull-sawtooth configuration, the reflective faces 162 are not equallyspaced. High reflectivity of the reflective faces 162 is achieved in oneembodiment by coating the diffraction grating 150 with gold. Inalternative embodiments, different reflective coatings, such asaluminum, are used. Further, although FIG. 1(b) shows the grating to beconfigured on a flat substrate 170, the invention more generallyincludes the use of curved substrates.

[0050] While the grating configuration shown in FIG. 1(a) withright-apex triangles 110 permits reflection of incident light from theside of the triangle 110 opposite the blaze angle θ_(b), thefull-sawtooth configuration using right-base triangles 160 shown in FIG.1(b) substantially restricts reflection to be from the reflective faces162. As a result, there is a significant reduction in boundary effectsfor P-polarized light as the electric field passes the apex of onetriangle 160 and reflects off the adjacent reflective face 162. Moregenerally, the support wall 164 is connected non-normally with thesubstrate 170, preferably forming an obtuse angle so that thecharacteristic of limiting reflection of incident light essentially onlyoff the reflective faces 162 and not off the support walls 164 ismaintained (see discussion below with regards to FIG. 9). The blazeangle θ_(b) at which the reflective faces 162 are inclined to thesubstrate surface is preferably in the range 50-70°, most preferably inthe range 50-60°. At a grating density 1/d=900 faces/mm, which is asuitable value for the 1530-1570 nm wavelength used for opticaltelecommunications signals, this is preferably θ_(b)=54.0°. At thisblaze angle, the product of the diffraction efficiencies in the S and Ppolarization configurations is maximized, as discussed below in thecontext of FIG. 4(a). This blaze angle is essentially different fromΦ≅sin⁻¹λ/2d (=43.5-45.0°), the angle of incidence at which the gratingefficiency is maximized. Thus, maximal grating efficiency for theinvention is achieved substantially away from the Littrow condition.

[0051] A second set of embodiments of the invention (referred to hereinas the “truncated-sawtooth” embodiments) is illustrated in FIG. 1(c). Inthese embodiments, which may also be used in first order, the steepnotch of the full-sawtooth embodiments is eliminated. In the particulartruncated-sawtooth embodiment illustrated in FIG. 1(c), the diffractiongrating 200 includes a plurality of reflective faces 212 each orientedat blaze angle θ_(b) with respect to a surface of the substrate 220.Each such reflective face 212 is supported by a support wall 214 that issubstantially normally connected with the surface of the substrate.Accordingly, the diffraction grating 200 has a configuration that usesmultiple right-base triangles 210, thereby sharing the advantage of thefull-sawtooth configuration in which the normal orientation of thesupport walls 214 mitigates boundary effects for P-polarized light asthe electric field of the light passes the apex of one triangle 210 andreflects off an adjacent reflective surface 212. More generally, thesupport walls 214 connect with the substrate 170 non-normally,preferably forming an obtuse angle so that the characteristic oflimiting reflection of incident light essentially only off thereflective faces 162 and not off the support walls 164 is maintained.

[0052] Such truncated-sawtooth embodiments may be characterized byrecognizing that each reflective face has an extent such that itsorthogonal projection on the substrate is less than the averageseparation between the reflective faces. Thus, a trench is definedbetween each support wall and the reflective face subsequent to thatsupport wall. In these embodiments, in addition to the blaze angle θ_(b)and line density 1/d, the grating may be characterized by the trenchwidth s and groove depth τ, both of these quantites being defined in thefigure, subject to the constraint${\tan \quad \theta_{b}} = {\frac{t}{d - s}.}$

[0053] While the full-sawtooth embodiments had no exposure of thesubstrate 170 at the base of the triangles 160, the truncated-sawtoothembodiments permit such exposure. In particular, surface portions 216 ofthe substrate 220 are exposed. The effect of permitting such exposureallows reduced altitude of right triangles 210. It is evident, however,that the full-sawtooth configuration is a limiting case of thetruncated-sawtooth configuration as the altitude of the triangles isincreased. For a grating density 1/d=900 faces/mm, this limit isapproached with a triangle altitude of approximately 1635 nm.

[0054] In one truncated-sawtooth embodiment, illustrated in FIG. 1(c),each of the reflective faces 212 is equally spaced along the surface ofthe substrate 220. In alternative embodiments such spacing may beirregular. Also, FIG. 1(c) shows each reflective face 212 extendingthrough substantially half of the spacing period, although otherfractions of the spacing period may also be used. In the illustratedembodiment, the blaze angle θ_(b) is also preferably in the range50-70°, most preferably in the range 50-60°. At opticaltelecommunications wavelengths, 1530-1570 nm, with a grating density1/d=900 faces/mm, this is preferably θ_(b)=55.8°. Again, this optimalblaze angle corresponds to the angle at which the product of diffractionefficiencies in the S and P polarization configurations is maximized, asdiscussed in the context of FIG. 4(b) below. As for the embodimentillustrated in FIG. 1(b), the maximal efficiency for the grating isachieved substantially away from Littrow conditions since this blazeangle is essentially different from (Φ≅sin⁻¹λ/2d (=43.5-45.0°), theangle of incidence at which the grating efficiency is maximized. Also,as for the first embodiment, the substrate 220 is shown to be flat onlyfor illustrative purposes. More generally, the invention includes theuse of a curved substrate.

[0055] Additionally, various reflective materials may be used and may bedifferently applied in various embodiments. For example, in oneembodiment, the entire diffraction grating 200 is coated with gold. Inalternative embodiments, different reflective coatings, such asaluminum, are used.

[0056] 4. Diffraction Efficiency of the Specific Embodiments

[0057] Various properties of the embodiments described above may beunderstood by examining the diffraction efficiency achieved by thegratings in various circumstances. The diffraction efficiency of adiffraction grating is generally a function of the wavelength of theoptical signal to be diffracted, and is defined as the ratio of theenergy of the diffracted wave to the energy of the incident wave:E=E_(out)/E_(in). As a rough approximation, for Littrow gratings themaximum efficiency is expected at the blaze wavelength λ_(b) with a 50%reduction at 0.7 λ_(b) and 1.8 λ_(b). For telecommunicationsapplications the range in wavelengths, 1530-1570 nm (i.e. 1550±1.3%), isconsiderably more narrow so that only relatively small variations inefficiency are expected as a function of wavelength. Furthermore, theefficiency in higher orders is expected to follow the general shape ofthe first-order efficiency curve, although the maximum efficiencygenerally decreases for each such higher order. Results for gratings inwhich the line density is configured for use in higher orders arediscussed below.

[0058] Accordingly, FIG. 2 shows the results of calculations of adiffraction efficiency profile in both the S and P polarizationconfigurations for the diffraction grating shown in FIG. 1(b) over awavelength range of 1530-1570 nm. A similar plot is produced in FIG. 3for the diffraction grating shown in FIG. 1(c). To evaluate the level ofuncertainty of the results, the calculations were performed with twocommercially available software packages: G-Solver (solid lines) andPC-Grate (dashed lines). For the calculations discussed below, PC-Grateand G-Solver have generally agreed within about 3% efficiencies, withoutany observable trend of one estimating higher efficiencies than theother.

[0059] Over the entire optical telecommunications wavelength range, thediffraction efficiency exceeds 85% for both S and P polarizations forboth the illustrated full-sawtooth and truncated-sawtoothconfigurations, with approximately less than a ±2% variation over thewavelength range for any given polarization. The explicit comparison ofthe two numerical packages in FIGS. 2 and 3 highlights their closeagreement, with differences no greater than about 3%. Considering thewavelength range of interest and both numerical programs, it can be seenthat the invention produces a high diffraction efficiency that issubstantially independent of polarization. For the particularfull-sawtooth embodiment illustrated in FIG. 1(b), thatpolarization-independent efficiency is 90±4%. The efficiency is evengreater for a truncated-sawtooth embodiment with θ_(b)55.8° and trianglealtitude (height of support wall 214) equal to 1310 nm. In thatembodiment, the efficiency is 94±4%, i.e. greater than 90% everywhere.

[0060] In FIG. 4(a) and FIG. 4(b), an illustration is made of how thenumerically calculated diffraction efficiency is used to determine theoptimal blaze angle. For the full-sawtooth embodiment, for example, FIG.4(a) shows the variation in efficiency for both the S and P polarizationconfigurations as a function of blaze angle as calculated with theG-Solver package. For these calculations, a grating density 1/d=900faces/mm was used with an angle of incidence for a 1550-nm opticalsignal of (Φ=45°. As described above, this particular incident angle Φis approximately the angle dictated by the Littrow condition. Theoptimal blaze angle is the angle where the curves for the S and Ppolarization intersect, i.e. where the product of the two efficienciesis maximized. For the full-sawtooth embodiment, this is seen to occur atθ_(b)=54.0°. Similarly, FIG. 4(b) shows the efficiencies for S and Ppolarizations for a truncated-sawtooth embodiment with triangles havingan altitude equal to 80% of the maximum possible altitude. Again, thecalculations were performed for a grating with grating density 1/d=900faces/mm and a 1550-nm optical signal incident at Φ=45°. For thisgrating, the curves cross at the optimal blaze angle θ_(b)=55.8°.

[0061] Results are summarized in FIG. 5 of the optimal blaze angle θ_(b)for a grating in the full-sawtooth embodiment. The calculations wereagain performed using the G-Solver package and show how the optimalblaze angle varies as a function of the grating density 1/d. Thecalculations were performed for an incident optical signal withwavelength λ=1550 nm and the incident angle was determined from theLittrow condition for each groove density plotted. The general trend,with the blaze angle increasing monotonically as a function of gratingdensity, is as expected.

[0062] The effect of moving the incident angle away from the Littrowcondition is illustrated in FIG. 6. The results of calculations for afull-sawtooth grating using the G-Solver package are shown. Thediffraction efficiency was calculated in both S and P polarizationconfigurations for an optical signal with wavelength λ=1550 nm onto agrating blazed at θ_(b)=54.0° with grating density 1/d=900 faces/mm. Thepreferred incident angle defined by the Littrow condition is Φ=44.2°.While the S-polarization efficiency varies little around this angle,dipping even slightly, the P-polarization efficiency shows a clearlydefined maximum at this angle such that the total efficiency ismaximized at this incident angle. Although not shown, similar resultsare also obtained when a truncated-sawtooth grating is used with itsoptimal blaze angle.

[0063] The variation in efficiency for the truncated-sawtoothembodiments for the S and P polarization states is shown respectively inFIGS. 7(a) and 7(b) as a function of the height of support wall 214. Theillustrated results were calculated for a blaze angle θ_(b)=55.8° forlight incident at Φ=45° with PC-Grate, although similar results areobtained with the G-Solver package. As can be readily seen, theS-polarization efficiency has two local maxima and the P-polarizationefficiency exhibits asymptotic behavior. Accordingly, the preferredtriangle altitude for the truncated-sawtooth configuration is at thesecond peak in the S-polarization efficiency, i.e. near 1310 nm.

[0064]FIG. 8 shows that the diffraction efficiency of both S and Ppolarization states is also dependent on the grating density 1/d. Thecalculations were performed with the G-Solver package for afull-sawtooth grating with optimal blaze angle θ_(b). The incidentoptical signal had wavelength λ and was incident at the angle defined bythe Littrow condition. To achieve a diffraction efficiency greater than90% simultaneously for both the S and P polarizations, it is preferablethat the grating density 1/d be between 700 and 1100 faces/mm. Morepreferably, the grating density is between 800 and 1000 faces/mm.

[0065] The numerical results presented in FIGS. 2-8 were calculated fordiffraction gratings that have the support walls connected with thesubstrate substantially normally. FIG. 9 shows that when the angle atwhich the support wall connects with the substrate (the “back angle”),is acute, the efficiency of the P-polarization configuration decreasessharply. The calculations were performed with the G-Solver package for afull-sawtooth grating having a grating density 1/d of 900 faces/mm and ablaze angle θ_(b) of 54.0°. As the figure shows, a decrease of the backangle from 90° results directly in a significant decrease inP-polarization diffraction efficiency. A decrease of the angle by about100 causes an efficiency decrease of about 10%. While the S-polarizationdiffraction efficiency shows some improvement in the region betweenabout 82 and 84°, it too drops off for more acute angles. If the backangle is obtuse, the diffraction efficiency is expected to be the sameas it is for a right back angle since the reduction in boundary effectsfor P-polarized light is maintained. Accordingly, it is preferred thatthe back angle be approximately ≧90°.

[0066] 5. Gratings for use in Hither Interference Orders

[0067] At telecommunications wavelengths, the grating embodimentsdescribed above are appropriate for use in at least the first order ofinterference. More generaly, however, the resolving power of the gratingis mN, where m is the order of interference and N is the number ofgrooves in the grating. Thus, in accordance with further embodiments, agrating is provided for use in nonunity orders of interference m bydecreasing the line density to 1/m times the line density used for firstorder. As before, for high dispersion with wavelengths for opticaltelecommunications applications in the range 1530-1570 nm, a value ofm/d between about 700 and 1100 faces/mm is desirable. Thus, for example,for a grating configured to be used in second order (m=2), a linedensity of 1/d between 350 and 550 faces/mm is appropriate for opticaltelecommunications wavelengths.

[0068] The manner in which light reflected from a diffraction grating isdistributed among the different orders of interference is determined bythe shape and orientation of the reflective faces. Thus, numericalcalculations exhibiting the properties of a grating for use in secondorder are shown in FIGS. 10-14. The calculations were performed with thesoftware package PC-Grate for a truncated-sawtooth grating as shown inFIG. 1(c) with a line density 1/d=450 faces/mm, which is midway withinthe range of 350-550 faces/mm appropriate for second order. For eachfigure, the incident angle for the optical signal was Φ45°.

[0069] FIGS. 10(a) shows the S-polarization diffraction efficiency insecond order for a truncated-sawtooth embodiment where the wavelength ofthe incident optical signal is λ=1545 nm. The results are presented as afunction of the trench width s between 0.4 and 0.8 μm for five differentvalues of the blaze angle θ_(b)=52.5°, 54.0°, 55.8°, 56.4°, and 57.0°.There are two features that are relevant to assessing the effectivenessof the grating. First, the peak in S-polarization efficiency is achievedfor increasing trench width s as the blaze angle is increased. Second,the value of that peak efficiency is maximized for a blaze angle ofθ_(b)=55.8°, the same optimal blaze angle determined for a 900 faces/mmgrating in first order.

[0070] A similar dependence for the P-polarization diffractionefficiency in second order is shown in FIG. 10(b). The P-polarizationefficiency is approximately flat over the range in trench widths shownin FIG. 10(a) for the S-polarization efficiency, dropping off at abouts=0.6 μm. Combining the results from FIGS. 10(a) and 10(b), an optimalblaze angle is found to be approximately 55.8°. Accordingly, FIG. 11reproduces the results from FIGS. 10(a) and 10(b) for θ_(b)=55.8°. It isevident from the figure that at this blaze angle, diffractionefficiencies in both the S and P polarizations may simultaneously bekept above 90% when the trench width s is between about 0.50 and 0.70μm.

[0071]FIG. 12 summarizes the average of diffraction efficiency resultsfor the S and P polarizations, simultaneously illustrating thedependence on the signal wavelength λ and the groove depth τ. As thefigure illustrates, the average efficiency may be maintained above 90%over a wavelength range between 1530 and 1560 nm for groove depths up to2400 nm and at least as low as 2300 nm. For wavelengths near the higherend of the range, the average efficiency may be maintained above 94% forgroove depths between 2300 and 2400 nm. Using the relationship relatingthe groove depth, trench width, blaze angle, and line density, where theline density is 1/d=450 faces/mm and the blaze angle is θ_(b)=55.8°, atrench width of s=0.63 μm (where the S-polarization efficiency ismaximized) corresponds to a groove depth of τ=2340 nm, and the maximumgroove depth of τ=2600 nm shown in FIG. 12 corresponds to a trench widthof s=0.45 μm.

[0072]FIG. 13 illustrates similar results for the polarization-dependentloss achieved with a grating having the same characteristics as thatused for FIG. 12: a line density of 1/d=450 faces/mm, a blaze angle ofθ_(b)=55.8°, and an incident signal angle of Φ=45°.Polarization-dependent loss results from the fact that the efficiency ofthe diffraction grating depends on the polarization state of theincident light. The electric field E of an arbitrarily polarizedincident optical signal may be written as a superposition of twoelectric fields linearly polarized along two orthogonal axes {circumflexover (p)} and ŝ, corresponding respectively to P and S polarizationdirections, i.e. parallel and perpendicular to the plane of incidence:

E=E _(p) {circumflex over (p)}+E _(s) ŝ

[0073] The intensity I₀ of the incident signal is defined by thestrength of the electric field along the orthogonal directions:${I_{0} = {\frac{1}{2}\sqrt{\frac{ɛ}{\mu}}\left( {{E_{p}}^{2} + {E_{s}}^{2}} \right)}},$

[0074] where ε and μ respectively denote the permittivity andpermeability of the medium. To simplify the discussion, units are chosenin which ε=4μ, so that the coefficient relating the intensity andsquared electric field is unity. The diffraction efficiency is governedby independent efficiency coefficients E in the orthogonal polarizationdirections such that the electric field E′ of the signal reflected bythe grating is

E′=−{square root}{square root over (E_(p))} E _(p){circumflex over(p)}−{square root}{square root over (E_(s))}E _(s){circumflex over (s)}

[0075] with total intensity

I′=E _(p) |E _(p)|² +E _(s) |E _(s)|²

[0076] It is thus evident that the intensity of a signal purely S or Ppolarized is reflected by the diffraction grating with an intensitydependent only on the efficiency coefficient for that direction:

I ^(p) =E _(p) |E _(p)|²

I ^(s) =E _(s) |E _(s) ²

[0077] Since in general E_(p)≠E_(s), there may be large variability inthe overall efficiency as a function of the polarization state of theincident signal.

[0078]FIG. 13 shows the degree of loss attributable to this polarizationdependence in decibels as a function both of signal wavelength andtrench depth. For all wavelengths in the range 1530-1560 nm, thepolarization-dependent loss is less than 0.4 decibels for a groove depthτ<2600 nm. Of particular note is a trench in the profile at t≈2500 nmwhere the polarization-dependent loss is everywhere less than about 0.04decibels. Thus, diffraction gratings configured in accordance withembodiments of the invention permit low polarization-dependent losses atoptical telecommunications wavelengths. Such low polarization-dependentloss characteristics may be achieved simultaneously with highdiffraction efficiencies in both S and P polarizations.

[0079]FIG. 14 provides a comparison of the diffraction efficiency andpolarization-dependent loss over a wavelength range of 1500-1600 nm fortwo different configurations of the diffraction grating. In bothinstances, the grating is configured for use in second order with agrating density 1/d of 450 faces/mm, with θ_(b)=55.8° and the opticalsignal incident at Φ=45°. In the first instance, the grating has aconstant trench width of s=528 nm (corresponding to a groove depth oft=2485 nm) and, in the second instance, the grating has a constanttrench width of s=533 nm (corresponding to a groove depth of t=2493 nm).The general behavior of the diffraction efficiency is the same in bothcases, with the average of efficiencies for the S and P polarizationsincreasing monotonically from about 80% at λ=1500 nm to about 94% atλ=1600 nm. The polarization-dependent loss includes a minimum, whichshifts from about λ=1525 nm at a trench width of s=528 nm up to aboutλ=1545 nm at a trench width of s=533 nm.

[0080] Each of the different embodiments may be preferable for differentapplications. For example, when the trench width is s=533 nm, it ispossible to maintain average efficiency over 85% over the wavelengthrange λ=1530-1570 nm while simultaneously keeping thepolarization-dependent loss under about 0.08 dB. For applications whereit is desirable to use the diffraction grating over the larger rangeλ=1500-1600 nm, a configuration with a trench width of s=528 nm providesan average efficiency everywhere greater than 80% and apolarization-dependent loss everywhere less than 0.15 dB.

[0081] 6. Grating Fabrication Process

[0082] A process in accordance with embodiments of the present inventionfor fabricating diffraction gratings with the characteristics describedabove is illustrated in FIG. 15. The process combines bothcrystalline-independent and crystalline-dependent etching techniqueswhile exploiting the crystalline characteristics of appropriatematerials. Techniques that rely solely on crystalline-dependent etchingtechniques, such as described in U.S. Pat. No. 4,330,175, filed Jul. 17,1979 by Fujii et al., which is herein incorporated by reference for allpurposes, can only produce grating profiles narrowly limited by thecrystallographic structure of the material used. The combination ofcrystalline-independent and crystalline-dependent techniques inaccordance with the present invention permit the grating pitch and angleto be varied independently.

[0083] As shown in FIG. 15(a), the process begins with a suitablecrystal surface 500 having a surface normal inclined at a tilt angle ψfrom an etch direction, such as from the [110] direction when thecrystal surface is a silicon surface, where the notation [jkl] is usedto denote the usual Miller indices. In one embodiment the crystalsurface is a wafer. The tilt angle ψ of the starting crystal surface 500is chosen to be complementary to the desired blaze angle θ_(b) of thefinal diffraction grating. Thus, for embodiments of the grating with ablaze angle in the approximate range 54°<θ_(b)<56°, the tilt angle is inthe approximate range 34°<ψ<36°. Silicon is one material withcrystallographic properties that permit such tilt angles and can be usedwith the combined crystalline-independent and crystalline-dependentetching process of the invention, although the use of any alternativematerial with suitable crystalline structure is also within the scope ofthe invention. In certain alternative embodiments, III-V or II-VIsemiconductor materials such as GaAs, IP, or ZnSe may be used instead ofa Group-IV semiconductor material.

[0084] A series of vertical trenches 510 are etched into the crystalsurface 500, as shown in FIG. 15(b). The spacing of the trenchescorresponds to the spacing of reflective faces in the resultingdiffraction grating; accordingly, equally spaced vertical trenches 510are etched for those embodiments in which a diffraction grating havingequally spaced reflective faces is produced. The etching technique usedto produce the vertical trenches 510 is a crystalline-independenttechnique, in the sense that its etch activity is irrespective of thecrystalline structure of the starting crystal surface 500. Oneappropriate technique for producing the vertical trenches 510 is toidentify the trench locations lithographically and then apply verticalreactive ion etching (“RIE”), a technique in which positively chargedions are accelerated towards the crystal surface 500. Alternativecrystalline-independent techniques also suitable for etching thevertical trenches 510 include ion milling and deep RIE (“DRIE”). Boththe vertical RIE and ion-milling techniques produce vertical trenches510 with substantially straight walls. DRIE produces a trench with acharacteristic inwards scalloping of the walls. Use of DRIE in this stepresults in a diffraction grating where the support walls 164 includethis inwards scalloping feature; since the side walls are not opticallyimportant for the grating, such scalloping is not objectionable.

[0085] The etched crystal surface is subsequently coated with asacrificial layer 515 as shown in FIG. 15(c). The sacrificial layer 515is deposited so that it fills the bottoms of the vertical trenches 510,where it is used to prevent excessive etching of the crystal surface inthe crystalline-dependent etch step described below (FIG. 15(e)). Thoseof skill in the art will appreciate that if the aspect ratio of thevertical trenches 510 is large, as may be desirable to limit the size ofthe mesas 525 described below, voids may form in the sacrificial layer515 within the vertical trenches 510 during deposition. Such voids donot significantly affect the process adversely provided there issufficient material at the bottom of the trenches to terminate thecrystalline-dependent etch step (FIG. 15(e)).

[0086] Appropriate materials for the sacrificial layer include oxides ornitrides such as SiO₂ or Si₃N₄.

[0087] The sacrificial layer 515 is subsequently patterned by etching itat locations that define the extent of the diffraction gratingsreflective faces. In the illustration in FIG. 15(d), the etched portions518 of the sacrificial layer 515 are formed adjacent to the verticaltrenches 510. The depth of the vertical trenches 510 formed during thecrystalline-independent etch (FIG. 15(b)) and the positions of theetched portions 518 of the sacrificial layer 515 are constrained so thatthey define parallel segments inclined with respect to the crystalsurface. The specific portions of the sacrificial layer 515 are etchedwith any appropriate lithographic and etching technique, for example byusing photoresist and RIE.

[0088] In FIG. 15(e) the effect of applying a crystalline-dependent etchthrough the patterned sacrificial layer 515 is shown. By using anetchant that preferentially etches along [110] orientations and notalong [111] orientations, inclined trenches 520 are formed in thecrystal. A suitable crystalline-dependent chemical etchant is KOH, whichhas an etching ratio between the [110] and [111] orientations thatexceeds 600. The structure of a material such as silicon includes manycrystallographic planes, leading to a concern that there may beinterference with other of such planes when the crystalline-dependentetch is applied. The inventors have recognized, however, that with theparticular crystallographic structure of silicon and similarlystructured materials, the etching can be limited to the desired [110]orientations. As a result, the inclined trenches 520 are etched withnegligible etching in undesirable directions. Alternativecrystalline-dependent chemical etchants that may also be used with asilicon crystal in accordance with the invention include hydrazine andethylene diamine pyrocatechol. The activity of the chemical etchant isstopped when it encounters the sacrificial layer 515 deposited withinthe vertical trenches 510.

[0089] After completion of the crystalline-dependent etching step, thecrystal surface 500 is exposed to an etchant that dissolves thesacrificial layer and is agitated to release the remaining sacrificiallayer portions and unattached pieces of the surface that may bediscarded. The profile of the resulting micromachined crystal surface500′ is shown in FIG. 15(f). This micromachined crystal surface 500′ maybe used directly to produce the diffraction grating or may be used as amaster for replication of diffraction gratings. When used directly, themesas 525 that result from the crystalline-independent etching stepproduce the truncated sawtooth profile shown in FIG. 1(c). When used asa master, the resulting diffraction grating (which has a profileinverted from the micromachined crystal surface 500′) has right-basetriangles 160 that are truncated at the apex as a result of the mesas525 in the master. Provided the size of this apical truncation is nottoo large, there are no significant adverse effects on the opticalproperties of the diffraction grating; the size of these mesas can belimited as desired by increasing the aspect ratio for the verticaltrenches 510. Whether the micromachined crystal surface 500′ is useddirectly or as a master, the grating is coated with a reflectiveoverlay, such as gold, which may be adhered to the grating with anadhesion layer such as titanium or chrome.

[0090] This specific etchant crystalline dependence is also used inalternative embodiments. In one such alternative embodiment, illustratedin FIG. 16, the initial steps are similar. First, as shown in FIG.16(a), the process begins with a suitable starting crystal surface 500having a surface normal inclined at tilt angle ψ from the [110]direction. As for the previous embodiment, a series of vertical trenches540 are etched into the crystal surface 500 with acrystalline-independent technique such as RIE [FIG. 16(b)]. Asacrificial material 545, such as SiO₂ or Si₃N₄, is subsequentlydeposited so as to fill the trenches [FIG. 16(c)]. In this embodiment,however, the top of the sacrificial layer 545 overlying the crystalsurface 500 is removed substantially completely after the depositionstep, producing the structure shown in FIG. 16(d). One technique thatmay be used to remove the material in this way is chemical andmechanical polishing (CMP). As can be seen in FIG. 16(d), this stillleaves the material deposited within the vertical trenches 510 to act asan etch stop. Application of the chemical crystalline-dependent etch asshown in FIG. 16(e) acts as before to etch preferentially along [110]orientations and not along [111] orientations. Termination of thecrystalline-dependent etch by the deposited sacrificial material 545thus produces the inclined surfaces. Subsequent removal of the remainingsacrificial material 545 to produce the micromachined surface 500″ shownin FIG. 16(f) is optional. Either the surface shown in FIG. 16(e) or thesurface shown in FIG. 16(i) may be used as described above to completeproduction of the diffraction grating.

[0091] In another alternative embodiment, the sacrificial layer 515 isnot deposited uniformly over the crystal surface 500; instead, suchmaterial is deposited within each of the trenches at a sufficient depthto act as an etch stop when the crystalline-dependent chemical etch isapplied. In still another alternative embodiment, the crystal surface500 is replaced with a silicon-on-insulator (“SOI”) layered structure,in which an insulator layer (e.g., an oxide layer) lies intermediatebetween underlying bulk silicon and an overlying epitaxial siliconlayer. The crystalline-independent etch of the vertical trenches 510 isperformed down to the insulator layer. As before, the vertical trenchesare protected by filling them with sacrificial material, and the processis otherwise performed as previously described. This embodimentsimplifies etching the vertical trenches 510 to substantially equaldepths.

[0092] Use of a crystalline-dependent chemical etchant produces anatomically smooth surface along the inclined trench 520, a feature thatis beneficial to the optical characteristics of the diffraction gratingbecause the reflective faces 112 are formed on this surface. Othertechniques to form the reflective faces, such as ion-beam etching (asdescribed in, e.g., U.S. Pat. No. 5,279,924, filed Jul. 1, 1992 by Sakaiet al., which is incorporated herein by reference for all purposes) failto produce atomically smooth surfaces so that the opticalcharacteristics of the diffraction grating are poorer. Anotherconsequence of ion-beam etching, such as shown in FIGS. 2-5 of U.S. Pat.No. 5,279,924, is an undesirable curvature of the grating profile at theintersection of the support walls and reflective faces.

[0093] Having described several embodiments, it will be recognized bythose of skill in the art that various modifications, alternativeconstructions, and equivalents may be used without departing from thespirit of the invention. Accordingly, the above description should notbe taken as limiting the scope of the invention, which is defined in thefollowing claims.

What is claimed is:
 1. A diffraction grating for diffracting an opticalsignal of wavelength λ in an interference order m higher than firstorder, the diffraction grating comprising: a substrate; and anarrangement of reflective faces oriented at respective blaze anglesθ_(b) spaced along a surface of the substrate with an average separationd, each reflective face being supported by a support wall, wherein theblaze angles θ_(b) substantially differ from the Littrow condition sinθ_(b)=mλ/2d, and wherein each reflective face has an extent such thatits orthogonal projection on the substrate is less than the averageseparation d, whereby a trench having a trench width s is definedbetween each support wall and the reflective face subsequent to thatsupport wall within the arrangement and a groove depth t is defined bythe altitude of the support wall with respect to the surface of thesubstrate.
 2. The diffraction grating according to claim 1 wherein theinterference order is second order m=2, the wavelength λ is within therange 1500-1600 nm, and the reflective faces are uniformly spaced at agrating density 1/d between 350 and 550 faces/mm.
 3. The diffractiongrating according to claim 2 wherein the grating density 1/d is between400 and 500 faces/mm.
 4. The diffraction grating according to claim 2wherein the grating density 1/d is substantially equal to 450 faces/mm.5. The diffraction grating according to claim 2 wherein each of theblaze angles θ_(b) is between 50° and 70°.
 6. The diffraction gratingaccording to claim 5 wherein each of the blaze angles θ_(b) is between50° and 60°.
 7. The diffraction grating according to claim 5 whereineach of the blaze angles θ_(b) is substantially equal to 55.8°.
 8. Thediffraction grating according to claim 7 wherein the trench width s ofeach trench is between 0.50 and 0.70 1 μm.
 9. The diffraction gratingaccording to claim 8 wherein the trench width s of each trench isbetween 0.55 and 0.65 μm.
 10. The diffraction grating according to claim7 wherein the groove depth t is between 2300 and 2500 nm.
 11. Thediffraction grating according to claim 10 wherein the groove depth t isbetween 2300 and 2400 nm.
 12. The diffraction grating according to claim10 wherein the groove depth t is between 2400 and 2500 nm.
 13. Thediffraction grating according to claim 1 wherein the diffraction gratingexhibits an average diffraction efficiency in S and P polarizationsexceeding 80% when the optical signal has wavelength λ in the range1500-1600 nm.
 14. The diffraction grating according to claim 13 whereinthe diffraction grating further exhibits a polarization-dependent lossless than 0.15 dB when the optical signal has a wavelength λ in therange 1500-1600 nm.
 15. The diffraction grating according to claim 1wherein the diffraction grating exhibits a polarization-dependent lossless than 0.15 dB when the optical signal has a wavelength λ in therange 1500-1600 nm.
 16. The diffraction grating according to claim 1wherein each of the plurality of reflective faces is comprised of a goldcoating.
 17. A diffraction grating for diffracting an optical signal ofwavelength λ, the diffraction comprising: a substrate; and anarrangement of reflective faces oriented at respective blaze anglesθ_(b) spaced along a surface of the substrate, wherein the arrangementof reflective faces is configured such that the optical signal isdiffracted with a polarization-dependent loss less than 0.4 dB when thewavelength λ is within the range 1500-1600 nm.
 18. A diffraction gratingaccording to claim 17 wherein the arrangement of reflective faces isconfigured such that the optical signal is diffracted with apolarization-dependent loss less than 0.15 dB when the wavelength λ iswithin the range 1500-1600 nm.
 19. A diffraction grating according toclaim 17 wherein the arrangement of reflective faces is configured suchthat the optical signal is diffracted with a polarization-dependent lossless than 0.10 dB when the wavelength λ is within the range 1530-1565nm.
 20. A diffraction grating according to claim 17 wherein thearrangement of reflective faces is configured such that the opticalsignal is diffracted with a polarization-dependent loss less than 0.04dB when the wavelength λ is within the range 1530-1565nm.
 21. A methodfor diffracting an optical signal of wavelength λ in an interferenceorder m higher than first order, the method comprising: propagating theoptical signal towards a plurality of reflective faces oriented atrespective blaze angles θ_(b) spaced along a surface of a substrate withan average separation d, each reflective face being supported by asupport wall, wherein the blaze angles substantially differ from theLittrow condition sin θ_(b)=mλ/2d, and wherein each reflective face hasan extent such that its orthogonal projection on the substrate is lessthan the average separation d, whereby a trench having a trench width sis defined between each support wall and the reflective face subsequentto that support wall within the arrangement and a groove depth t isdefined by the altitude of the support wall with respect to the surfaceof the substrate; and reflecting the optical signal off the plurality ofreflective faces.
 22. The method according to claim 21 wherein theinterference order is second order m=2, the wavelength λ is within therange 1500-1600 nm, and the reflective faces are uniformly spaced at agrating density 1/d between 350 and 550 faces/mm.
 23. The methodaccording to claim 22 wherein the grating density 1/d is between 400 and500 faces/mm.
 24. The method according to claim 22 wherein the gratingdensity 1/d is substantially equal to 450 faces/mm.
 25. The methodaccording to claim 22 wherein each of the blaze angles θ_(b) is between50° and 70°.
 26. The method according to claim 25 wherein each of theblaze angles θ_(b) is between 50° and 60°.
 27. The method according toclaim 25 wherein each of the blaze angles θ_(b) is substantially equalto 55.8°.
 28. The method according to claim 27 wherein the trench widths of each trench is between 0.50 and 0.70 μm.
 29. The method accordingto claim 28 wherein the trench width s of each trench is between 0.55and 0.65 μm.
 30. The method according to claim 27 wherein the groovedepth t is between 2300 and 2500 nm.
 31. The method according to claim30 wherein the groove depth t is between 2300 and 2400 nm.
 32. Themethod according to claim 30 wherein the groove depth t is between 2400and 2500 nm.
 33. The method according to claim 21 wherein reflecting theoptical signal off the plurality of reflective faces comprisesreflecting the optical signal with an average diffraction efficiency inS and P polarizations exceeding 80% when the optical signal has awavelength λ in the range 1500-1600 nm.
 34. The method according toclaim 33 wherein reflecting the optical signal off the plurality ofreflective faces further comprises reflecting the optical signal with apolarization-dependent loss less than 0.15 dB when the optical signalhas a wavelength λ in the range 1500-1600 nm.
 35. The method accordingto claim 21 wherein reflecting the optical signal off the plurality ofreflective faces further comprises reflecting the optical signal with apolarization-dependent loss less than 0.15 dB when the optical signalhas a wavelength λ in the range 1500-1600 nm.
 36. The method accordingto claim 21 wherein each of the plurality of reflective faces iscomprised of a gold coating.
 37. A method for diffracting an opticalsignal of wavelength λ the method comprising: propagating the opticalsignal towards an arrangement of reflective faces oriented at respectiveblaze angles θ_(b) spaced along a surface of a substrate; and reflectingthe optical signal off the arrangement of reflective faces with apolarization-dependent loss less than 0.4 dB when the wavelength λ iswithin the range 1500-1600nm.
 38. The method according to claim 37wherein reflecting the optical signal comprises reflecting the opticalsignal off the arrangement of reflective faces with apolarization-dependent loss less than 0.15 dB when the wavelength λ iswithin the range 1500-1600 nm.
 39. The method according to claim 37wherein reflecting the optical signal comprises reflecting the opticalsignal off the arrangement of reflective faces with apolarization-dependent loss less than 0.10 dB when the wavelength λ iswithin the range 1530-1565 nm.
 40. The method according to claim 37wherein reflecting the optical signal comprises reflecting the opticalsignal off the arrangement of reflective faces with apolarization-dependent loss less than 0.04 dB when the wavelength λ iswithin the range 1530-1565 nm.